Abstract
The radial factorR(x, x s ) of a scalar field in Schwarzschild's space-time satisfies a second order ordinary differential equation with two regular singular points atx=0 andx=x s and one irregular singular point atx=∞. The analytical properties of four solutions ℛ1, ℛ2, ℛ3, and ℛ4 (defined by their power series expansions aboutx=0 andx=x s ) with respect tox s are studied. An analytical continuation is given for each solution outside its circle of convergence. Relations to the flat-space solutions are established. Finally the coefficients relating linearly any three of these solutions are determined and studied as functions of the parameterx s .
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Communicated by J. Ehlers
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Persides, S. Global properties of radial wave functions in Schwarzschild's space-time. Commun.Math. Phys. 48, 165–189 (1976). https://doi.org/10.1007/BF01608503
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DOI: https://doi.org/10.1007/BF01608503